2-1Please draw the kinematic diagrams of the mechanisms shown below。
(a)(b)(c)2-2 Please calculate the DOF of mechanisms as follows, can you point out these mechanisms have a determined motion or not ? (The link with arrow is driving link)（d ）（c ）3-1 Please confirm the location of the instant centres of mechanisms as follows（Using the signP）。
ij4-1According to the link dimension ,determine the type of four-bar linkage holding different link as frame？4-2 In a revolute four-bar linkage ABCD shown as below b=100mm c=80mm d=110mm(1)Find the range of the values for the length L AB of link AB if the linkage is either (a) crank-rocker mechanism with crank AB ,or(b) a double-rocker mechanism.(2) Can the linkage be a double-crank mechanism by choosing L AB suitably?Why?4-3 In the double-crank linkage ABCD shown as below L AB=80mm L BC=180mm L CD=230mm L AD=200 The driver BC rotates at a constant speed. Find the minimum transmission angleof the linkagemin4-4 In the revolute four-bar linkage ABCD Let link AD is the frame L AB=60mm L BC=130mm L CD=140mm L AD=200mm and 0BAD∠=135(1)Determine the type of the revolute four-barmechanism(2) If the side link AB is a driver and rotates at aconstant speed(a)find the pressure angle αand transmission angle γof the mechanism at that position(b) Find the angularϕstroke of the link CDmax(c) Find the crank acute angleθbetween the twolimiting positions(d) Calculate the time ratio K(e) Will any dead-point occur during the whole cycle ofthe motion?(f) Find the maximum pressure angleαand themax minimum transmission angleγmin4-5 Design the revolute four-bar linkage ABCD according to the figure as below:Let the length of rocker L CD =75mm , L AD=100mm and Link AD is the frame , the time ratio K=1.5 , The angle between one limiting position of rocker and the frame 045∠=CDACalculate the length of L AB、L BC（has two results）4-6 Design the offset slider-crank mechanism ABC according to the figure as below: The crank AB is the driver, Let the length of crank L AB =25mm, The offset e=10mm, The maximum pressure angle 0max 30α= Find the stroke H of the slider and the crank acute angleθ between the two limiting positions.4-7 图所示为一牛头刨床的主传动机构，已知mm l AB 75=，mm l D E 100= ，行程速比系数K=2，刨头5的行程H=300mm ，要求在整个行程中，推动刨头5有较小的压力角，试设计此机构。
5-1 For the plate cam with translating offset knife-edge follower Let the lift mm h 4.2=，cam angle for rise00120δ=，cam angle for outer dwell 0s 60δ=，camangle for return 00120δ'=，cam angle for inner dwell 0s 60δ'=.The follower rise as constant acceleration anddeceleration motion curve ；and return as cosine acceleration motion curve.Please draw the displacement curve of the follower.5-2For the plate cam with translating offset knife-edge follower shown as belowPlease draw the displacement curve of the follower by graphical method5-3 图示为一偏置滚子从动件盘形凸轮机构。
已知凸轮轮廓由三段圆弧和一直线组成，它们的圆心分别O 、O /及O //，半径分别为mm r mm r mm r 536,18=''='=及，偏距e=8mm 。
滚子半径mm r T 5=。
现要求：1）、画出凸轮的理论轮廓曲线及基圆；2）、求出从动件的行程h 、推程运动角a δ及回程运动角c δ； 3）、标出图示位置从动件的位移s 及凸轮机构的压力角α； 4）、标出凸轮由图示位置转过600时，从动件的位移S /及凸轮机构的压力角α'。
6-1 For the figure shown as below ，Let the radius of base circle mm r b 30= The radius of curvature of the involute at the point K mm K K mm r k 15,35==，Find ：1) The radius of curvature of the involute at the point K /k r 'and the pressure angle k α'。
2) if k r k r '''=。
Calculate the length of arc K K '''.6-2 An involute standard spur gear has parameters Z=26, m=3mm, h*a=1,0α=. Find the radii of curvature of20tooth profile on the reference circle and the tip circle and the pressure angle on the tip circle6-3 A pair of standard spur involute gears has a moduleof 5mm, pressure angle 020α=,center distancea=350mm, transmission ratio 129/5i =.Calculate the numbers of teeth Z 1,Z 2,reference diameters d 1,d 2,addendumdiametersd a1,d a2,basediametersd b1,d b2,tooth thickness s and spacewidth e.6-4 For a pair of external standard spur gears pressure angle 020α=, module m=20mm, Z 1=30, Z 2=40.(1)Calculate the working pressure angle α' when the working center distance is a /=725mm.(2)If the working pressure angle 02230α''=,find the center distance is a /.6-5 For a pair of external standard spur gears020αα'==, m=5mm, Z 1=19, Z 2=42.Calculate the contact ratioαε6-6 已知一对外啮合变位齿轮传动，1221==Z Z ，m=10mm ，020＝α，mm a h a 130,1*='=，试设计这对齿轮传动(列表给出两轮的),,,,,,,s d d d d h h y b f a f a ，并验算重合度及齿顶圆齿厚（S a 应大于0.25m ，取21x x =）。